Fig 1.
User interface of the Lifespan model.
The interface was designed to offer information on the go during the computations allowing the model to be stopped, the protocol to be modified and the programme to be run again from the start. Running the Lifespan model with defaults generates the “Reference” output (Fig 3), analysed in detail in the text. The “Change Reference State” tag calls up a window with options for controlling the initial condition of the cell; the “Change PIEZO parameters” tag brings up the window for setting the PIEZO1-mediated permeabilities and the duration of the open-state. Three additional tags implement instructions for running (Run) and stopping (Stop) the computations and for generating csv files at the end of a run (Save csv) with the results displayed in the same format as that described before [1]. The main user interface is divided in three main panels: the top-right panel lists five time-dependent values, from top to bottom: Lifespan duration (h), data-output periodicity (min; defaulted to 1440, one output per day), rate constants of exponential decay for the Na/K (kNaP) and calcium pumps (kCaP; 1/min), and delayed onset time for Na/K pump decay (TNaP; min). In the running of the Lifespan model, selected data appear listed in the top left panel: Time (in min), Relative cell volume (RCV), membrane potential (Em, mV), Na/K pump-mediated Na efflux (FNaP, mmol/Loch), Trans-CCa (μmol/Loc), Trans-Hct (%), and number of model cycles in between data points (iterations). Trans-labelled variables report values at the end of the last capillary transit for the time point listed under Time. Selected variables are shown in graphic format in the bottom panel, clockwise from top left: RCV, CNa & CK & CA (mmol/Loc), pHi, and EK (the potassium equilibrium potential, mV). All default values for parameters and initial variables correspond to those used for the pattern defined by the Reference lifespan curve (Fig 3). The “Save csv” tag generates two csv files to enable comparisons between variables that change between the end of capillary transit (Transit-named csv file) and the end of intertransit periods for each time point: CVF/Ht, CCa, CCa2+, CH, MNa, MK, MA, MH, FCaP, FKGardos and all FzX ([1], Appendix]).
Fig 2.
Testing the quantal hypothesis; predicted changes in Relative Cell Volumes at different PzCa levels.
The trends shown only for the first thirty days remained unchanged for 120 days. Pump decay rate constants were set to zero. Triangles: effects of increasing JS turnover rate five-fold at PzCa = 70/h. Note that even at the highest PzCa shown, final dehydration does not exceed 10% of initial RCV.
Fig 3.
Pattern of change in relative cell volume and density over a standardized 120 day lifespan period that best represents available evidence.
The lines join data points collected at daily intervals. The Lifespan model was run with the cell volume fraction set at 0.9 during the brief capillary transit period. “Restore medium” was set to YES to prevent carryover changes in medium concentrations during inter-transit periods. RCV: Relative cell volume, a convention adopted in RBC homeostasis models to report RBC volumes relative to a standardized value of 1 L/Loc attributed to a RBC defined with 0.75 Lcw/Loc, 0.25 LHb/Loc and 340 gHb/Loc (User Guide, Appendix). Density: Density profile, in g/ml. The initial condition of the cell was defined with Vw of 0.85 Lcw/Loc, CNa of 5 mM, CK of 145 mM, and a Na/K pump-mediated Na+ efflux rate of -3.2 mmol/Loch, an approximate representation of the condition of a recently transitioned cell from reticulocyte to mature RBC with its full complement of haemoglobin set at 340 gHb/Loc. The parameter values used were: OS, 0.4s; PzCa, 70/h; PzA, 50/h (no significant differences between 30/h and 50/h for PzA, the range observed under on-cell patch clamp [19]); kCaP, 8e-6/min; kNaP, 3e-5/min; TNaP, 115200min; PzNa and PzK were set to zero. The RCV curve is used as a standardized reference (Ref) for analysing the effects of parameter variations in Figs 4 and 5.
Fig 4.
Effect of changes in PIEZO1-mediated ionic permeabilities (Pz) and pump decay rates (kP) on the lifetime pattern of cell volume change.
1. The parameter values for Reference curve 1 (black) are as reported in the legend of Fig 3. 0: With PzX = 0 and no pump decay the model computes a flat response over the full 120 days period demonstrating the robust stability of the Lifetime computations. 7: With the PzX set as for the reference curve (curve 1) but with no pump decay (curve 7, kP OFF) there is no progressive dehydration-densification, only the early quantal dehydration reported in Fig 2. 6: With PzX = 0 and pump decays set to ON (curve 6, Pz0, kP ON) there is no dehydration phase, only late hydration following delayed Na/K pump decay. 5: Same as curve 1 but with PzA set to zero showing how extremely limiting the anion permeability can be to both initial and cumulative dehydration responses. 4: Relatively minor reductions in PzCa from 70/h (Curve 1) to 60/h (curve 4) reduce initial and cumulative dehydration responses outside observed ranges. 2 & 3: Large changes in PIEZO1-mediated Na+ and K+ permeabilities, curves 2 and 3, have relatively minor effects, mostly on the timing and magnitude of the late density reversal response, rendering the Lifespan model a poor predictor of their likely real values. 8: Protocol identical to that of reference curve 1 but for a cell defined in the RS with a FCaPmax of 24 instead of 12 mmol/Loch; the increased pump strength reduced the extent of early dehydration and in order to approximate the reference dehydration pattern as shown it was necessary to increase kCaP from 8e-6 to 1.25e-5 min-1.
Fig 5.
Effects of pump decay rates and timings, and of Gardos channel inhibition on the predicted lifetime pattern of cell volume change.
Parameter changes are listed relative to reference curve 1. For the simulation shown in curve 6 the Gardos channel Fmax was changed from 30/h to zero in the Reference State. For curves 3 and 4 TNaP was set to zero and the decay rates to 7e-6/min and 1e-5, respectively. For curves 2 and 5 PMCA decay rates were set to 1e-5 and 5e-6, respectively.
Fig 6.
Predicted lifespan changes in the intracellular concentrations of Na (CNa), of K (CK) and of diffusible anions A (CA) for the conditions of the Reference pattern (Fig 3).
Note that because PzNa and PzK were set at zero in the minimalistic representation of the reference pattern, the predicted changes shown in this figure result solely from the cumulative effects of periodic Gardos channel activation and Na/K pump decay.
Fig 7.
Predicted lifespan changes in cell pH (pHi) and in the intracellular concentrations of permeant anions A- (CA) and of H+ (CH) for the conditions of the Reference pattern (Fig 3).
Besides minor contributions from variations in haemoglobin buffering, most changes in CH are driven primarily by changes in the anion concentration gradient (rA) acting through the Jacob-Stewart mechanism causing rH to approach rA during periods between capillary transits (User Guide). At constant MA all anion gradient changes apply to CA, thus generating similar time-courses for CA and pHi (Panel A), or mirror image changes for CA and CH (Panel B).
Fig 8.
Predicted changes in RBC volume (A), and in cell concentrations (B) of K(CK), of Na(CNa), and of permeant anions (CA) during hyperdense collapse induced by elevated PzCa. The changes induced by setting PzCa = 80/h (red curves) are compared with those of the reference pattern with PzCa = 70/h (black curves).
Fig 9.
Effects of high and low cell volume fractions (CVF) during capillary transits on the lifespan patterns of changes in cell volume and [Ca2+]i.
Reference pattern (black) modelled with CVF of 0.9 during capillary transits. Test curves (red and green) modelled with CVF of 0.00001 throughout transit-intertransit periods. PMCA decay rates (kCaP), as indicated in the figure (in min-1). Note how the reduction in kCaP from 8e-6 (red) to 6e-6 (green) prevents hyperdense collapse at CVF 0.00001 and restores pattern towards Reference curve (black). Inset: [Ca2+]i values (CCa2+) recorded at the end of PIEZO1 open states on the last model iteration of each day (col 19 of the transit csv files). Note the increasing divergence between REF (black) and low-CVF (red) curves leading to hyperdense collapse. Late reversal of [Ca2+]i results from terminal rehydration of the cells.
Fig 10.
Simulating the lifespan of a seven day irreversible sickle cell (ISC), showing the predicted changes in RCV (black) and density (red), (panel A), and in the cell concentrations (panel B) of K(CK), of Na(CNa), and of permeant anion (CA). The parameters used were: Lifespan duration, 168h (7 days); Data output periodicity: 60m; kNaP, 2e-3/m; kCaP, 5e-5/m; TNaP, 5760m (4 days); PIEZO1 open state, 30s; PzCa, 5.7/h; PzA, 50/h; PzNa, 0; PzK, 0.